Piecewise immunosuppressive infection model with viral logistic growth and effector cell-guided therapy

This work investigated a piecewise immunosuppressive infection model that assessed the effectiveness of implementing this therapeutic regimen once the effector cell count falls below a specific threshold level by introducing a threshold strategy. The sliding mode dynamics, global dynamics, and boundary equilibrium bifurcations of the Filippov system were examined based on the global dynamics of the two subsystems. Our primary findings indicate that the HIV viral loads and effector cell counts can be stabilized within the required predetermined level. This outcome depends on the threshold level, immune intensity, and the initial values of the system. Therefore, properly combining these key factors makes it possible to effectively curb the abnormal increase of virus and keep the effector cells at a reliable level. This approach maximizes the controllable range of the HIV. The proposed switching system incorporating pseudo-equilibrium exhibits three types of equilibriums that could be bistable or tristable. It means there is a possibility of controlling the virus after administering therapy if the immune intensity $ c $ is limited within the range of the post-treatment control threshold and the elite control threshold when $ {R_0} > {R_{{c_1}}} > {R_{{c_2}}} > 1 $.